1. Introduction2. Main Definitions and Notations3. Filtering and Smoothing Recursions4. Advanced Topics in Smoothing5. Applications of Smoothing6. Monte Carlo Methods7. Sequential Monte Carlo Methods8. Advanced Topics in Sequential Monte Carlo9. Advanced Topics in Sequential Monte Carlo10. Advanced Topics in Sequential Monte Carlo11. Maximum Likelihood Inference, Part II:Monte Carlo Optimization12. Statistical Properties of the MaximumLikelihood Estimator13. Fully Bayesian Approaches14. Elements of Markov Chain Theory15. An Information-Theoretic Perspective onOrder Estimation